# Systems of linear forms and covers for star bodies

Acta Arithmetica (1992)

- Volume: 61, Issue: 2, page 119-127
- ISSN: 0065-1036

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top## How to cite

topM. M. Dodson. "Systems of linear forms and covers for star bodies." Acta Arithmetica 61.2 (1992): 119-127. <http://eudml.org/doc/206455>.

@article{M1992,

author = {M. M. Dodson},

journal = {Acta Arithmetica},

keywords = {metric diophantine approximation; systems of linear forms; cover; star body; Hausdorff dimension},

language = {eng},

number = {2},

pages = {119-127},

title = {Systems of linear forms and covers for star bodies},

url = {http://eudml.org/doc/206455},

volume = {61},

year = {1992},

}

TY - JOUR

AU - M. M. Dodson

TI - Systems of linear forms and covers for star bodies

JO - Acta Arithmetica

PY - 1992

VL - 61

IS - 2

SP - 119

EP - 127

LA - eng

KW - metric diophantine approximation; systems of linear forms; cover; star body; Hausdorff dimension

UR - http://eudml.org/doc/206455

ER -

## References

top- [1] J. D. Bovey and M. M. Dodson, The fractional dimension of sets whose simultaneous rational approximations have errors with a small product, Bull. London Math. Soc. 10 (1978), 213-218. Zbl0384.10013
- [2] J. D. Bovey and M. M. Dodson, The Hausdorff dimension of systems of linear forms, Acta Arith. 45 (1986), 337-358. Zbl0534.10025
- [3] J. W. S. Cassels, An Introduction to the Geometry of Numbers, Grundlehren Math. Wiss. 99, Springer, Berlin 1959.
- [4] M. M. Dodson, A note on the Hausdorff-Besicovitch dimension of systems of linear forms, Acta Arith. 44 (1985), 87-98.
- [5] M. M. Dodson, Star bodies and Diophantine approximation, J. London Math. Soc. 44 (1991), 1-8.
- [6] H. G. Eggleston, Sets of fractional dimensions which occur in some problems of number theory, Proc. London Math. Soc. 54 (1951-1952), 42-93. Zbl0045.16603
- [7] K. J. Falconer, The Geometry of Fractal Sets, Cambridge Tracts in Math. 85, Cambridge University Press, Cambridge 1985.
- [8] P. Gruber and C. G. Lekkerkerker, Geometry of Numbers, North-Holland, Amsterdam 1987. Zbl0611.10017
- [9] W. K. Hayman, Meromorphic Functions, Oxford Math. Monographs, Clarendon Press, Oxford 1964.
- [10] V. Jarník, Über die simultanen diophantischen Approximationen, Math. Z. 33 (1931), 505-543. Zbl57.1370.01
- [11] H. Rüssmann, On the one-dimensional Schrödinger equation with a quasi-periodic potential, Ann. New York Acad. Sci. 357 (1980), 90-107.
- [12] V. G. Sprindžuk, Metric Theory of Diophantine Approximations, translated by R. A. Silverman, V. H. Winston & Sons, Washington, D.C., 1979. Zbl0287.10043
- [13] K. Yu, Hausdorff dimension and simultaneous rational approximation, J. London Math. Soc. 24 (1981), 79-84 Zbl0427.28008

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